Post-distortion tone shaping in the MT-2 Metal Zone

[ElectricDruid]

Hi all,

I've been studying the Boss MT-2 Metal Zone pedal. I've turned up something which seems a bit weird, and I wondered if anyone else could shed any light. I'm looking at the post-distortion tone shaping stage:



Now, this is a pair of gyrators, and we can enter the component values in the very-handy tool over on Muzique.com:
http://www.muzique.com/lab/gyrator.htm

The LHS gyrator gives sensible values: 4898Hz, with a Q of 2.2. Call it a peak at 5KHz.

The RHS gyrator gives far more Q than I expect: 105Hz, with a  of 14.6

What's going on here? Am I wrong in thinking 14.6 is a ridiculously high Q? (It's a bandwidth of 1/10th of an octave)

Any light you can shed would be appreciated.

Thanks,
Tom

[PBE6]

Just tried in the simulator and the numbers are right, but it is a bit strange. 105 Hz corresponds to a G#, 4th fret on the 6th string. You'd figure that if they wanted to nail any particular note it would be an E instead.

[ElectricDruid]

EDIT: Solved this - see below. Updated images reflect the new situation with the missing resistor included.

ORIGINAL:
There is something else that strikes me as odd too. The "High" control claims to be a 15dB cut/boost, and to be honest, that is how the circuit looks. But try as I might, I can only get boost in the simulation:





Any ideas?

Thanks,
Tom

[PBE6]

This looks just like RG's parametric EQ with two bands.

When the pot is turned so the HIGH wiper is touching the -ve input, the circuit acts as a shelving high pass gain stage. The maximum boost is about 1+22k/2.2k = 11 = 21 dB, until it gets up into the 700 kHz range where the gain drops back to 0 dB.

When the wiper is touching the +ve input, the circuit acts as a frequency-dependent voltage divider, which would be a first order low pass filter (EDIT: oops, it's a shelving cut and not a first order LP) that starts rolling off above 7.2kHz (if the impendance of the previous stage is basically resistive). However, if the previous impedance is very small then the voltage divider (R + Zc) / (R + Zc + Zp) becomes (R + Zc) / (R + Zc) = 1 and there is no filter effect.

This is the likely culprit, try adding a resistor to the output of the previous stage and see what happens.

[PRR]

> wrong in thinking 14.6 is a ridiculously high Q?

Q=14 is silly high.

BUT look what happens in-circuit. C020 and gyrator are a series L-C circuit. Impedance goes to zero at resonance, except R027 spoils it by 470 Ohms. This works against opamp 4B and its 3.3K resistor.

OFF-resonance, gyrator stuff is infinite, 4B works unity gain.

ON-resonance, 4B gives gain of 1+(3.3K/470) or 8.

There's no direct comparison, but an 8X bump is not typical of a HIGH Q resonance. High, but not silly high.

Is there a bass-cut before this? (Typical of many heavy distortions.) Then the C020+gyrator may "just" be bringing-up the bass which was cut before. 105Hz is a reasonable "bottom note". Yes, you have a 82Hz note, but many-many guitar speakers won't reproduce that, or blattt when they are forced to. An all-users designer may compromise several notes higher, knowing that most users have a bassist all-over the bottom octave, and don't need real balls below 100Hz or so.
_________________________

> "High" control .... I can only get boost

There HAS to be a resistor cut-off where your snippet shows "In".

With HIGH at "1", R061 C044 will load-down whatever feeds this.

But if the source is a SPICE generator (infinite power), you can not load it down.

Even a TL0xx? won't load-down enuff to notice.

And I submit that the missing resistor is same-as R015. (see why?)

[PBE6]

Makes sense if it's a 22k resistor like R015, then at high frequencies the voltage divider becomes 2.2k / (2.2k + 22k) = 1/11 = -21 dB and is symmetrical in terms of boost/cut magnitude. It also puts the "flat" spot in the middle of the pot rotation where you expect it to be.

[ElectricDruid]

Ah, excellent! Thanks everyone! That's it. I forgot that damn resistor off the input. And yes, it's the same as the other one.

WRT to the initial query about the high Q, ok, x8 gain sounds *more* reasonable. I did a sim of this stage too, and the frequency response looked ok in the sim, but there I get a gain of 5dB for that lower peak - not even x2, let alone x8. So I still can't make it match up.



Of course, I might have left a resistor out of this one too

Yes, there is some bass-cut on the previous stage. Or two stages previously, anyway. The pre-distortion tone shaping is a broadish mid hump, so both treble and bass take a knock at that point. That stage probably accounts for some of the divisive "nasal" character of the pedal.

Tom

[PRR]

> the high Q

R030 damps the resonator.

Reactance of L or C is somewhat above 6K at 105Hz. 3.3K is heavy damping.

[ElectricDruid]

> the high Q

R030 damps the resonator.

Reactance of L or C is somewhat above 6K at 105Hz. 3.3K is heavy damping.

Sorry, I don't understand this. What aren't I getting?

This is what I think is going on. Please tell me when I go off the rails:
The gyrator is wired up as a resonant circuit, a notch. At resonance, its resistance will drop to the value of the gyrator feedback resistor R027/470R. This gives the figure of x8 gain you mentioned. Far from its resonant frequency, the resistance will be the resistor to ground, 470K. This gives a gain of as close to x1 as makes no odds.

So where does 6K come from? I don't see this at all, but gyrators are a black box to me for the most part.

Thanks for the help,
Tom

[PRR]

> where does 6K come from?

What is the reactance of 0.22uFd at 105Hz? Looks like 6,893r to me. ("6K" was a hasty-guess.)

The "L" (gyrator) must be the same at resonance.

This looks-into R030 3.3K. The leverage here is not so clear at the moment. However if the nominal reactances are ~~6.9K at resonance, anything "like" 3.3K across that is a low Q.

[PRR]

Here is a plot of the tank impedance.



The "bottom" is higher than 470 exact. The 470K also appears as a loss, reflected around the reactance value at resonance, another 101 Ohms. In the practical circuit, transistor emitter impedance will be another 50-100 Ohms.

Note that the reactances are below 3.3K in the range from 83Hz-133Hz. Still working on just what that means.

[PRR]

> I did a sim of this stage too, ...I get a gain of 5dB for that lower peak

Show your work (circuit).

I get 16.6dB. This is without the upper resonator; I'm not seeing why it would make much difference.

[ElectricDruid]

Ok, here's what I've got. I started with the full stage, but I've also tried it with just the one that's baffling me to see if the upper gyrator makes any difference to it. It doesn't.






I also wondered if the AC-coupling cap HPF (1u/100K) or the feedback cap 47p made any difference, although they shouldn't. I tried it without them anyway- no difference. Whatever's going on is because of the gyrator, or how I have it set up.

Thanks,
Tom

[PRR]

> here's what I've got.

Thanks for playing along.

I believe your circuit is correct.

When I replace the perfect follower with a transistor, I get ~~5dB bump.

When I increase transistor hFE insanely large, 7dB.

When I run the transistor on 40V, 10dB.

The mandated Q of 14 is *far* beyond what any practical single transistor can do. Even at 1.5mA and hFE=25,000.

So the "ideal gyrator calculator"s assumptions are invalid, and it gives a wrong answer.

Also a warning. We know the product sold and presumably sounded fine to developer and users. This is one case where an "obvious minor improvement", an opamp in place of the emitter follower, will give very different and possibly blattty result.

At Q nearer "1", the gyrator does work well with either opamp or EF.

EDIT: when I trim my "gain of 1.0000000" block to gain of 0.967, it matches the stock transistor form. Falling just a few % shy of 1.000... hammers the bump down a lot.

[ElectricDruid]

Thanks for playing along.

No, thank you for helping.

I believe your circuit is correct.

Well, that's a good start!

When I replace the perfect follower with a transistor, I get ~~5dB bump.

When I increase transistor hFE insanely large, 7dB.

When I run the transistor on 40V, 10dB.

The mandated Q of 14 is *far* beyond what any practical single transistor can do. Even at 1.5mA and hFE=25,000.

So the "ideal gyrator calculator"s assumptions are invalid, and it gives a wrong answer.

Also a warning. We know the product sold and presumably sounded fine to developer and users. This is one case where an "obvious minor improvement", an opamp in place of the emitter follower, will give very different and possibly blattty result.

At Q nearer "1", the gyrator does work well with either opamp or EF.

EDIT: when I trim my "gain of 1.0000000" block to gain of 0.967, it matches the stock transistor form. Falling just a few % shy of 1.000... hammers the bump down a lot.

That's pretty much what I suspected, but I couldn't prove it. My LTSpice skills are pretty basic. But I do know that transistor gyrators don't perform as well as op-amp ones, so my suspicion was that the theoretical Q of 14 was to compensate/allow for the vagaries of the transistor.

Since your x0.967 result shows that this circuit is very sensitive to gain variations of only a few percent, presumably the type or quality of transistor used would also make a difference.

What happens if the Q is less? Does the hump actually go *up* as it gets wider, because the transistor is better able to cope? (like the other gyrator) I'll have to try it I suppose. (Having understood, now it's time to start tweaking!)

I've been doing a full analysis and write-up on this circuit, and this was my last query, so I think I understand it all now. Thanks everso much for the help, Paul. It's been really useful.

Tom

[PRR]

> presumably the type or quality of transistor used would also make a difference.

Slight. As I said, bumping the '2222 tranny to 4X the current or 100X the hFe made few-dB change, no big change. Clearly switching from hFE=250 to hFE=500 is almost insignificant.

> What happens if the Q is less?

"At Q nearer "1", the gyrator does work well with either opamp or EF."